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Determination of suitable thin layer drying curve modelfor some vegetables and fruits

Ebru Kavak Akpinar *

Mechanical Engineering Department, Firat University, 23279 Elazig, Turkey

Received 16 August 2004; accepted 7 January 2005

Available online 25 February 2005

Abstract

This study presents a mathematical modeling of thin layer drying of potato, apple and pumpkin slices in a convective cyclone

dryer. In order to estimate and select the appropriate drying curve equation, 13 different models, which are semi-theoretical

and/or empirical, were applied to the experimental data and compared according to their coefficients of determination ( r,v2), which

were predicted by non-linear regression analysis using the Statistica Computer Program. Moreover, the effects of drying air temper-

ature, velocity and sample area on the model constants and coefficients were also studied by multiple regression analysis.

Consequently, of all the drying models, a semi-theoretical MidilliKucuk model was selected as the best one, according to r and v2.

2005 Elsevier Ltd. All rights reserved.

Keywords: Drying; Thin layer; Mathematical modelling

1. Introduction

Drying of moist materials is a complicated process

involving simultaneous, coupled heat and mass transfer

phenomena, which occur inside the material being dried

(Yilbas, Hussain, & Dincer, 2003).

Thin layer drying mean to dry as one layer of sample

particles or slices. Thin layer drying models that describe

the drying phenomenon of agricultural materials mainly

fall into three categories, namely theoretical, semi-theo-

retical and empirical (Midilli, Kucuk, & Yapar, 2002;

Panchariya, Popovic, & Sharma, 2002). The first takesinto account only internal resistance to moisture transfer

while the other two consider only external resistance to

moisture transfer between product and air (Bruce,

1985; Ozdemir & Devres, 1999; Parti, 1993). The most

widely investigated theoretical drying model has been

Ficks second law of diffusion. Drying of many food

products such as rice (Ece & Cihan, 1993) and hazelnut

(Demirtas, Ayhan, & Kaygusuz, 1998) has been success-

fully predicted using Ficks second law. Semi-theoretical

models offer a compromise between theory and ease of

use (Fortes & Okos, 1981). Simplifying general series

solution of second law Ficks or modification of simpli-

fied models generally derives semi-theoretical models.

But they are only valid within the temperature, relative

humidity, and airflow velocity and moisture content

range for which they were developed. They require small

time compared to theoretical thin layer models and donot need assumptions of geometry of a typical food, its

mass diffusivity and conductivity (Parry, 1985). Among

semi-theoretical thin layer drying models, the Newton

model, Page model, the modified Page model, the

Henderson and Pabis model, the logarithmic model,

the two-term model, the two-term exponential, the diffu-

sion approach model, the modified Henderson and Pabis

model, the Verma et al. model and the MidilliKucuk

model are used widely (Table 2). Empirical models derive

0260-8774/$ - see front matter 2005 Elsevier Ltd. All rights reserved.

doi:10.1016/j.jfoodeng.2005.01.007

* Tel.: +90 424 237 5343; fax: +90 424 241 5526.

E-mail addresses: [email protected], [email protected]

www.elsevier.com/locate/jfoodeng

Journal of Food Engineering 73 (2006) 7584
mailto:[email protected]:[email protected]:[email protected]:[email protected]

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a direct relationship between average moisture content

and drying time. They neglect fundamentals of the dry-

ing process and their parameters have no physical mean-

ing. Therefore they cannot give clear accurate view of the

important processes occurring during drying althoughthey may describe the drying curve for the conditions

of the experiments (Ozdemir & Devres, 1999). Among

them, the Wang and Singh model (see Table 2) has been

found application in the literature.

Recently, there have been many studies on the thin

layer drying and mathematical modeling of various veg-

etables, fruits and agro-based products such as potato

(Diamante & Munro, 1993), onion (Rapusas & Driscoll,

1995; Sarsavadia, Sawhney, Pangavhane, & Singh,

1999), hazelnut (Ozdemir & Devres, 1999), green pep-

per, green bean and squash (Yaldiz & Ertekin, 2001),

tea (Panchariya et al., 2002), green chilli (Hossain &Bala, 2002), banana (Dandamrongrak, Young, &

Mason, 2002), pistachio (Midilli & Kucuk, 2003) red

pepper (Akpinar, Bicer, & Yildiz, 2003). Moreover, the

effects of some parameters related to the product or dry-

ing conditions such as slice thickness, drying air temper-

ature, relative humidity, etc. were investigated by many

researchers (Hossain & Bala, 2002; Midilli & Kucuk,2003; Midilli et al., 2002; Ozdemir & Devres, 1999;

Sarsavadia et al., 1999; Yaldiz & Ertekin, 2001).

The main objective of this study was to determine

and test the most appropriate thin layer drying model

for understanding the drying behavior of potato, apple

and pumpkin slices.

2. Materials and methods

2.1. Experimental set-up

Fig. 1 illustrates the schematic diagram of the cyclone

type dryer, developed for experimental work (Akpinar,

Nomenclature

A sample area, the area having the product be-

fore drying process start, m2

a, b, c,g, h, n empirical constants in the drying models

k, k0, k1 empirical coefficients in the drying modelsn number constants

N number of observations

MR moisture ratio

MRexp experimental moisture ratio

MRpre predicted moisture ratio

M local moisture content, %dry basis

Mt mean moisture content at t, %dry basis

Me mean equilibrium moisture content, %dry

basis

Mi initial moisture content, %dry basisr correlation coefficient

r the diffusion path (m)

t time, min

T temperature, C

V velocity, m/s

v2 chi-square

Fig. 1. Experimental set-up: 1Drying chamber; 21st tray; 32nd tray; 4digital balance; 5Observed windows; 6digital thermometer; 7

the balance bar; 8control panel; 9thermocouples; 10digital thermometer and channel selector; 11rheostat; 12resistance; 13fan; 14wet

and dry thermometers; 15adjustable flab; 16duct; 17the outlet of air from dryer.

76 E.K. Akpinar / Journal of Food Engineering 73 (2006) 7584

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2002). The system was introduced in the literature

(Akpinar, Midilli, & Bicer, 2003). Briefly, it consists of

fan, resistance and heating control systems, air-duct,

drying chamber in cyclone type, and measurement

instruments. The heating system consisted of an electric

4000 W heater placed inside the duct. The rectangular

duct included air fan and resistance was constructedfrom sheet iron in 1000 mm length, 200 mm width and

250 mm height. The drying chamber was constructed

from sheet iron in 600 mm diameter and 800 mm height

cylinder. The inside and outside surfaces of the drying

chamber was painted with a spray dye to prevent rust

in the sheet iron surface. The drying chamber was con-

structed in concentric form and 30 mm annulus was iso-

lated by polystyrene. Both topside and bottom side of

drying chamber was closed. Also, the covers made

of the steel were isolated by polystyrene. This top

cover was used to load or unload the chamber. In the

measurements of temperatures, J type ironconstantan

thermocouples were used with a manually controlled

20-channel automatic digital thermometer (ELIMKO,

6400, Turkey), with reading accuracy of 0.1 C. A

thermo hygrometer (EXTECH, 444731, China) was

used to measure humidity levels at various locations of

the system. A 015 m/s range anemometer (LUTRON,

AM-4201, Taiwan) measured the velocity of air passing

through the system. Moisture loss was recorded at

20 min intervals during drying for determination of dry-

ing curves by a digital balance (BEL, Mark 3100, Italy)

in the measurement range of 03100 g and an accuracy

of 0.01 g.

2.2. Procedure

Before drying process, the products were peeled, po-

tato and apple cut into slices of 12.5 12.5 25 mm

and 8 8 18 mm (width thickness length) and

pumpkin cut into slices of 5 mm thickness and 35 mm

diameters with a mechanical cutter. The trays were

loaded as thin layer. The first weight of the potato, apple

and pumpkin was approximately 250, 125 and 200 g,

respectively. The product slices were carefully and or-

derly placed on the trays that are made of nylon so that

the airflow could pass across the trays. The initial andfinal moisture contents of the products were determined

at 80 C by using an Infrared Moisture Analyzer (MET-

TLER, LJ16, Switzerland). After the dryer is reached at

steady state conditions for operation temperatures, the

samples are put on the trays of dryer and dried there.

Drying experiments were carried out at 60, 70, and

80 C drying air temperatures and 1, 1.5 m/s drying air

velocities. The velocities and temperatures were mea-

sured in the centre of drying chamber. In the velocity

measurements, the values of the velocity in the centre

of the drying chamber were taken into account. The tan-

gential airflow was across the layer during drying pro-

cess. Drying was continued until the final moisture

content of the potato, apple and pumpkin reached to

approximately 10% (wb), 13% (wb), 6% (wb), respec-

tively. During the experiments, ambient temperature

and relative humidity, inlet and outlet temperatures of

drying air in the duct and dryer chamber were recorded.

Drying air was tangentially entered in drying chamber.

In this way, the samples were dried in swirl flow in place

of uniform flow. The flow diagram of the thin layer dry-

ing process is presented in Fig. 2.

2.3. Experimental uncertainty

Errors and uncertainties in the experiments can arise

from instrument selection, condition, calibration, envi-

ronment, observation, and reading, and test planning

(Akpinar, 2002; Akpinar et al., 2003). In drying

Fig. 2. The flow diagram of thin layer drying process of products.

E.K. Akpinar / Journal of Food Engineering 73 (2006) 7584 77

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experiments of the apple slices, the temperatures, veloc-

ity of drying air, weight losses were measured with

appropriate instruments. During the measurements of

the parameters, the uncertainties occurred were pre-

sented in Table 1.

3. Mathematical modeling of drying curves

It has been accepted that drying phenomenon of the

biological products during the falling rate period is con-

trolled by the mechanism of liquid and/or vapour diffu-

sion. This behavior suggested strongly an internal mass

transfer type drying with moisture diffusion as the con-

trolling phenomena. Assuming that the resistance to

moisture flow is uniformly distributed throughout the

interior of the homogeneous isotropic material, the dif-

fusion coefficient, D is independent of the local moisture

content and if the volume shrinkage is negligible, Fickssecond law can be derived as follows (Khraisheh,

Cooper, & Magee, 1997):

dM

dt D

d2M

dr21

where, M is the local moisture content (kg water/kg dry

solids), r is the diffusion path (m), t is the time (s) and D

is the moisture dependent diffusivity (m2/s).

Crank (1975) gave the analytical solutions of Eq. (1)

for various regularly shaped bodies such as rectangular,

cylindrical and spherical.

With the appropriate initial and boundary conditions

t 0; 0 < r< L; M Mi

t> 0; r 0;dM

dt 0

t> 0;

r

L;

M

Me

The solution of Eq. (1) for a slice, for a constant diffu-

sivity, D, in terms of infinite series is given in literature.

MR Mt MeMi Me

8

p2

X1n1

1

2n 12exp

2n 12p2Dt

4L2

" #2

where, MR is the fractional moisture ratio, Mi is the ini-

tial moisture, Mt is the mean moisture at time t, Me is

the mean moisture at equilibrium and L is the half thick-

ness of the slice for drying from both sides or the thick-

ness of the slice for drying from one sides.

For slices shapes, the first boundary condition states

that moisture is initially uniformly distributed through-

out the sample. The second implies that the mass trans-

fer is symmetric with respect to the centre of the slice.

The third conditions states that the surface moisture

content of the samples instantaneously reaches equilib-

rium with the conditions of surroundings air.

The theoretical and the semi-theoretical models are

summarized in Table 2. Semi-theoretical thin layer dry-

ing models are generally derived by simplifying general

series solution of Ficks second law. For example, the

Henderson and Pabis model is the first term of a generalseries solution of Ficks second law (Doymaz, 2005). For

mathematical modeling, the thin layer drying models in

Table 2 were tested to select the best model for describ-

ing the drying curve equation of potato, apple and

pumpkin slices during drying process by the convective

type cyclone dryer (Akpinar et al., 2003; Diamante &

Munro, 1993; Hossain & Bala, 2002; Midilli & Kucuk,

Table 1

Uncertainties of the parameters during drying of products

Parameter Unit Comment

Uncertainty in the temperature

measurement

Fan inlet temperature C 0.3800.576

Heaters outlet temperature C 0.576

Cyclone inlet temperature C 0.380Cyclone outlet temperature C 0.380

Centre temperature of product C 0.380

Temperature between of trays C 0.380

Ambient air temperature C 0.380

Inlet of fan with dry and wet

thermometers

C 0.5590.707

Uncertainty in the time measurement

Mass loss values min 0.1

Temperature values min 0.1

Uncertainty in the mass loss measurement g 0.5

Uncertainty in the air velocity measurement ms1 0.14

Uncertainty of the measurement of relative

humidity of air

RH 0.1

Uncertainty in the measurement of moisture

quantity

g 0.001

Uncertainty in reading values of table

(q, cp. . .)

% 0.10.2

Table 2

Thin layer drying curve models

Model name Model

Newton MR = exp(kt)Page MR = exp(ktn)Modified Page MR = expb(kt)ncModified Page MR = expb(kt)ncHenderson and Pabis MR = a exp(kt)Logarithmic MR = a exp(kt) + cTwo term MR = a exp(k0t) + b exp(k1t)Two-term exponential MR = a exp(kt) + (1a)exp(kat)Wang and Singh MR = 1 + at + bt2

Di ffusion approac h MR = a exp(kt) + (1a)exp(kbt)Modified Henderson

and Pabis

MR = a exp(kt) + b exp(gt) + c exp(ht)

Verma et al. MR = a exp(kt) + (1a)exp(gt)MidilliKucuk MR = a exp(ktn) + bt


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2003; Midilli et al., 2002; Mujumdar, 1995; Ozdemir &

Devres, 1999; Yaldiz & Ertekin, 2001). The regression

analysis was performed using Statistica Computer

Program. The correlation coefficient (r) was primary cri-

terion for selecting the best equation to describe the dry-

ing curve equation (Guarte, 1996; Midilli et al., 2002). In

addition to r, the reduced chi-square (v2

) was used todetermine the best fit (Midilli & Kucuk, 2003). This

parameter can be calculated as following:

v2

Pn

i1MRexp;i MRpre;i2

N n3

where, MRexp,i is the ith experimentally observed mois-

ture ratio, MRpre,i the ith predicted moisture ratio, Nthe

number of observations and n is the number constants

(Midilli et al., 2002; Sarsavadia et al., 1999).

Modeling the drying behavior of different agricultural

products often requires the statistical methods of regres-

sion and correlation analysis. Linear and non-linear

regression models are important tools to find the rela-tionship between different variables, especially, for

which no established empirical relationship exists. In

this study, the constants and coefficients of the best fit-

ting model involving the drying variables such as tem-

perature, velocity of the drying air and product size

were determined. The effects of these variables on the

constants and coefficients of drying expression were also

investigated by multiple linear regression analysis.

4. Results and discussion

Potato slices of 83% (wb), apple slices of 87% (wb),

pumpkin slices of 93% (wb) average initial moisture con-

tent were dried to 10% (wb), 13% (wb), 6% (wb), respec-

tively, at temperatures of 60, 70 and 80 C in the

velocities of drying air of 1 and 1.5 m/s by using a con-

vective dryer. The final moisture contents represent

moisture equilibrium between the sample and drying

air under dryer conditions, beyond which any changes

in the mass of sample could not occur.

The moisture content data at the different drying con-

ditions were converted to the more useful moisture ratio

expression and then curve fitting computations with the

drying time were carried on the 13 drying models evalu-

ated by the previous workers (see Table 2). The statisti-cal analyses results applied to these models at drying

process at 80 C drying air temperature and 1.5 m/s dry-

ing air velocity are given in Table 3 for potato slices,

apple slices and pumpkin slices. The best model describ-

ing the thin layer-drying characteristic was chosen as the

one with the highest r-value and the lowest v2 values.

From Table 3, it was determined that r = 0.99989,

v2 = 1.79 105 for potato slices, r = 0.99996, v2 =

1.00 105 for apple slices, r = 0.99967, v2 = 8.38

105 for pumpkin slices by the MidilliKucuk model.

The results have shown that the v2 values of the

MidilliKucuk model lower than the values determined

Table 3

Values of the drying constants and coefficients of different models determined through regression method for potato, apple and pumpkin slices

T= 80 C, V= 1.5 m/s; 1st tray Potato (12.5 12.5 25) Apple (12.5 12.5 25) Pumpkin

Model name R v2 R v2 R v2

Newton 0.99871 1.88 104 0.99875 2.35 104 0.98973 2.14 103

Page 0.99942 8.92 105 0.99930 1.43 104 0.99930 1.55 104

Modified Page 0.99942 8.92 105 0.99930 1.43 104 0.99930 1.55 104

Modified Page 0.99871 1.97 104 0.99876 2.53 104 0.98973 2.26 103

Henderson and Pabis 0.99915 1.30 104 0.99885 2.34 104 0.99235 1.69 103

Logarithmic 0.99917 1.34 104 0.99993 1.6 105 0.99757 5.72 104

Two term 0.99970 5 105 0.99885 2.76 104 0.99235 1.91 103

Two-term exponential 0.99970 5.56 105 0.99869 2.68 104 0.98952 2.31 103

Wang and Singh 0.95661 6.63 103 0.98977 2.07 103 0.99902 2.17 104

Diffusion approach 0.99970 4.77 105 0.99941 1.31 104 0.99912 2.08 104

Modi fied Henderson and Pabis 0.99970 5.56 105 0.99885 3.38 104 0.99234 2.21 103

Verma et al. 0.99969 4.78 105 0.99940 1.31 104 0.99911 2.09 104

Midilli and Kucuk 0.99989 1.79 105 0.99996 1.00 105 0.99967 8.38 105

T=60C Potato

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800

Drying time (min)

V = 1.5 m/s, 8x8x18 mm, 1st trayV = 1.5 m/s, 8x8x18 mm, 2nd trayV = 1.5 m/s, 12.5x12.5x25 mm, 1st trayV = 1.5 m/s, 12.5x12.5x25 mm, 2nd trayV = 1 m/s, 8x8x18 mm, 1st trayV = 1 m/s, 8x8x18 mm, 2nd trayV = 1 m/s, 12.5x12.5x25 mm,1st trayV = 1m/s, 12.5x12.5x25 mm, 2nd trayMidilli-Kucuk modelDiffusion approach model

MR=(M

t-M

e)/(M

i-M

e)

Fig. 3. Variation of the experimental and predicted moisture ratio by

the MidilliKucuk model and diffusion approach model with drying

time at 60 C of drying air for potato slices.


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by other models. It was noticed that the MidilliKucuk

model gave the highest r and the lowest v2 for all drying

conditions. Figs. 311 present the variations of moisture

ratio versus drying time for potato, apple and pumpkin

slices dried at the different drying air temperatures,

velocities and sample size. Additionally, Figs. 311 show

the comparison of experimental and predicted moistureratio by the MidilliKucuk model and the model has

correlation coefficient and chi-square, which is near to

this model. The results of non-linear regression analyses

and of statistical analyses applied to the MidilliKucuk

model for all drying conditions have shown in Table 4

for potato slices, Table 5 for apple slices, Table 6 for

pumpkin slices. Generally, r-values obtained by using

this model were varied between 0.999770.99995 for

potato slices, 0.999650.99997 for apple slices and

0.999400.99985 for pumpkin slices (see Tables 46).

As shown in Figs. 311, the MidilliKucuk model

showed good agreement with the experimental data

and gave the best results for potato, apple and pumpkin

slices according to r and v2. Therefore, the Midilli

Kucuk was selected to represent the thin layer-drying

behavior of these agricultural products according to

the highest r and the lowest v2. Consequently, it can

be said that the MidilliKucuk model could sufficiently

define the thin layer drying of potato, apple and pump-

kin slices.

T=70C Potato

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 50 100 150 200 250 300 350 400 450 500 550 600 650 700

Drying time (min)

V=1.5 m/s, 8x8x18 mm, 1st trayV=1.5 m/s, 8x8x18 mm, 2nd trayV=1.5 m/s, 12.5x12. 5x25 mm, 1st trayV=1.5 m/s, 12.5x12. 5x25 mm, 2nd trayV=1 m/s, 8x8x18 mm, 1st trayV=1 m/s, 8x8x18 mm, 2nd trayV=1 m/s, 12.5x12.5x25 mm, 1st trayV=1 m/s, 12.5x12.5x25 mm, 2nd trayMidilli-Kucuk modelDiffusion approach model

MR=(Mt-

Me

)/(Mi-

Me)

Fig. 4. Variation of the experimental and predicted moisture ratios bythe MidilliKucuk model and diffusion approach model with drying


T=80 C Potato

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 50 100 150 200 250 300 350 400 450 500 550 600 650

Drying time (min)

V=1.5 m/s, 8x8x18 mm, 1st trayV=1.5 m/s, 8x8x18 mm, 2nd trayV=1.5 m/s, 12.5x12.5 x25 mm, 1st trayV=1.5 m/s, 12.5x12.5 x25 mm, 2nd trayV=1 m/s, 8x8x18 mm, 1st trayV=1 m/s, 8x8x18 mm, 2nd trayV=1 m/s, 12.5x12.5x25 mm, 1st trayV=1 m/s, 12.5x12.5x25 mm, 2nd trayMidilli-Kucuk modelDiffusion approach model

MR=(M

t-M

e)/(M

i-M

e)

Fig. 5. Variation of the experimental and predicted moisture ratios by

the MidilliKucuk model and diffusion approach model with drying


T=60C Apple

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 50 100 150 200 250 300 350 400 450 500 550

Drying time (min)

V=1.5 m/s, 8x8x18 mm, 1st trayV=1.5 m/s, 8x8x18 mm, 2nd trayV=1.5 m/s, 12.5x12.5x 25 mm, 1st trayV=1.5 m/s, 12.5x12.5 x25 mm, 2nd trayV=1 m/s, 8x8x18 mm, 1st t rayV=1 m/s, 8x8x1 8 mm, 2n d trayV=1 m/s, 12.5x12.5x25 mm, 1st trayV=1 m/s, 12.5x12.5x25 mm, 2nd trayMidilli-Kucuk modelLogarithmic model

MR=(Mt-

Me)

/(Mi-

Me

)


the MidilliKucuk model and Logarithmic model with drying time at

60 C of drying air for apple slices.

T=70 C Apple

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 50 100 150 200 250 300 350 400 450 500

Drying time (min)

V=1.5 m/s, 8x8x18 mm, 1st trayV=1.5 m/s, 8x8x18 mm, 2nd trayV=1.5 m/s, 12.5x12.5x2 5 mm, 1st trayV=1.5 m/s, 12.5x12.5x2 5 mm, 2nd trayV=1 m/s, 8x8x18 mm, 1st trayV=1 m/s, 8x8x18 mm, 2nd trayV=1 m/s, 12.5x12.5x25 mm, 1st trayV=1 m/s, 12.5x12.5x25 mm, 2nd trayMidilli-Kucuk modelLogarithmic

MR=(M

t-M

e)/(M

i-M

e)





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The fitting procedure indicated that the mentioned

results of the MidilliKucuk model could be used to

model the thin layer drying behavior of these agricul-

tural products, but it did not indicate the effect of dryingconditions. To take into account the effect of the drying

variables on the MidilliKucuk model constants a, k, n

and b were regressed against those of drying air temper-

ature, velocity and sample area using multiple regression

analysis. All possible combinations of the different dry-

ing variables were tested and included in the regression

analysis. Based on the multiple regression analysis, the

accepted model, the constants and coefficients were as

follows:

MRa; k; b; t Mt MeMi Me

a expktn bt 4

where

for potato,

a 0:986173 0:000069 T 0:005702 V 0:098206 A 5k 0:015582 0:000156 T 0:013467 V 0:266761 A 6

n 1:218379 0:000802 T 0:162776 V 138:525 A 7

b 0:0000085 0:00000029 T 0:0000393 V 0:0203022 A

8

for apple,

a 1:004084 0:000073 T 0:001960 V 3:944759 A 9

k 0:006391 0:000065 T 0:009775 V 1:576723 A 10

n 1:187734 0:002467 T 0:128878 V 202:536 A 11

b 0:000082 0:000002 T 0:000041 V 0:041667 A 12

T=80 C Apple

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 50 100 150 200 250 300 350 400

Drying time (min)

V=1.5 m/s, 8x8x18 mm, 1st trayV=1.5 m/s, 8x8x18 mm, 2nd trayV=1.5 m/s, 12.5x12.5x 25 mm, 1st trayV=1.5 m/s, 12.5x12.5 x25 mm, 2nd trayV=1 m/s, 8x8x18 mm, 1st t rayV=1 m/s, 8x8x1 8 mm, 2 nd trayV=1 m/s, 12.5x12.5x25 mm, 1st trayV=1 m/s, 12.5x12.5x25 mm, 2nd trayMidilli-Kucuk modelLogarithmic model

MR=(M

t-M

e)/(M

i-M

e)




T=60 C Pumpkin

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800

Drying time (min)

V=1.5 m/s, 1st tray

V=1.5 m/s, 2nd tray

V=1 m/s, 1st tray

V=1 m/s, 2nd tray

Midilli-Kucuk model

Page model

MR=(M

t-M

e)/(M

i-M

e)


the MidilliKucuk model and Page model with drying time at 60 C of

drying air for pumpkin slices.

V=1.5 m/s, 1st tray

V=1.5 m/s, 2nd tray

V=1 m/s, 1st tray

V=1 m/s, 2nd tray

Midilli-Kucuk model

Page model

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 50 100 150 200 250 300 350 400 450 500 550 600

Drying time (min)

T=70C Pumpkin

MR=(Mt-

Me)/(Mi-

Me

)


the MidilliKucuk model and Page model with drying time at 70 C of

drying air for pumpkin slices.

T=80C Pumpkin

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 50 100 150 200 250 300 350 400 450 500

Drying time (min)

V=1.5 m/s, 1st tray

V=1.5 m/s, 2nd tray

V=1 m/s, 1st tray

V=1 m/s, 2nd tray

Midilli-Kucuk model

Page model

MR=(M

t-M

e)/(M

i-M

e)

Fig. 11. Variation of the experimental and predicted moisture ratios

by the MidilliKucuk model and Page model with drying time at 80 C

of drying air for pumpkin slices.


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Table 4

Values of the drying constant and coefficients of the MidilliKucuk model determined through regression method for potato slices at all drying

conditions

Drying air

temperature T, C

Air flow

rate V, m/s

Sample

area A, m2Tray no. a k n b r v2

80 1.5 0.000544 1 0.9989 0.0169 0.9804 0. 000052 0.99994 1. 17 105

70 1.5 0.000544 1 0.9995 0.0166 0.9457 0. 000048 0.99989 2. 05 105

60 1.5 0.000544 1 0.9989 0.0149 0.9351 0. 000038 0.99994 1. 01 105

80 1.5 0.001250 1 0.9973 0.0170 0.8893 0. 000051 0.99989 1. 79 105

70 1.5 0.001250 1 1.0069 0.0176 0.8484 0. 000049 0.99980 3. 14 105

60 1.5 0.001250 1 0.9957 0.0134 0.8459 0. 000075 0.99980 2. 93 105

80 1 0.000544 1 1.0001 0.0115 1.0214 0. 000041 0.99993 1. 25 105

70 1 0.000544 1 0.9991 0.0080 1.0594 0. 000018 0.99993 1. 03 105

60 1 0.000544 1 0.9968 0.0085 1.0109 0. 000022 0.99995 7. 65 106

80 1 0.001250 1 0.9966 0.0120 0.9153 0. 000041 0.99993 9. 73 106

70 1 0.001250 1 0.9971 0.0117 0.8992 0. 000038 0.99992 1. 19 105

60 1 0.001250 1 0.9963 0.0084 0.9283 0. 000034 0.99995 6. 33 106

80 1.5 0.000544 2 0.9996 0.0171 0.9686 0. 000016 0.99994 9. 05 106

70 1.5 0.000544 2 0.9985 0.0149 0.9559 0. 000049 0.99984 2. 98 105

60 1.5 0.000544 2 0.9967 0.0161 0.9095 0. 000030 0.99992 1. 15 105

80 1.5 0.001250 2 0.9977 0.0174 0.8756 0. 000045 0.99985 1. 86 105

70 1.5 0.001250 2 1.0047 0.0158 0.8564 0. 000051 0.99987 1. 98 105

60 1.5 0.001250 2 1.0016 0.0119 0.8623 0. 000074 0.99977 3. 53 105

80 1 0.000544 2 0.9976 0.0100 1.0341 0. 000017 0.99992 1. 28 105

70 1 0.000544 2 0.9991 0.0080 1.0594 0. 000018 0.99995 8. 63 106

60 1 0.000544 2 0.9936 0.0058 1.0678 0. 000025 0.99990 1. 72 105

80 1 0.001250 2 0.9963 0.0093 0.9568 0. 000022 0.99994 8. 68 106

70 1 0.001250 2 0.9957 0.0087 0.9438 0. 000032 0.99990 1. 53 105

60 1 0.001250 2 0.9934 0.0071 0.9532 0. 000034 0.99991 1. 29 105

Table 5

Values of the drying constant and coefficients of the MidilliKucuk model determined through regression method for apple slices at all drying

conditions

Drying air

temperature T, C

Air flow

rate V, m/s

Sample

area A, m2Tray no. a k n b r v2

80 1.5 0.000544 1 0.9987 0.0167 1.0520 0.000185 0.99990 3.50 105

70 1.5 0.000544 1 0.9970 0.0140 1.0325 0.000156 0.99974 7.63 105

60 1.5 0.000544 1 0.9988 0.0164 0.9681 0.000130 0.99995 1.11 105

80 1.5 0.001250 1 1.0014 0.0126 0.9893 0.000137 0.99996 1.00 105

70 1.5 0.001250 1 1.0028 0.0147 0.9348 0.000051 0.99987 2.42 105

60 1.5 0.001250 1 1.0003 0.0157 0.8898 0.000046 0.99990 1.67 105

80 1 0.000544 1 0.9991 0.0112 1.1375 0.000078 0.99997 9.35 105

70 1 0.000544 1 0.9990 0.0076 1.1481 0.000119 0.99991 2.63 105

60 1 0.000544 1 0.9996 0.0058 1.1445 0.000057 0.99997 7.29 106

80 1 0.001250 1 1.0011 0.0108 0.9859 0.000098 0.99994 1.20 105

70 1 0.001250 1 0.9988 0.0125 0.9261 0.000108 0.99993 1.30 105

60 1 0.001250 1 1.0076 0.0115 0.9145 0.000056 0.99982 3.00 105

80 1.5 0.000544 2 0.9971 0.0164 1.0546 0.000130 0.99965 1.16 104

70 1.5 0.000544 2 0.9993 0.0121 1.0514 0.000123 0.99994 1.71 105

60 1.5 0.000544 2 0.9982 0.0118 1.0220 0.000072 0.99991 2.14 105

80 1.5 0.001250 2 0.9998 0.0116 1.0021 0.000110 0.99992 1.86 105

70 1.5 0.001250 2 1.0018 0.0144 0.9277 0.000076 0.99982 3.40 105

60 1.5 0.001250 2 0.9990 0.0140 0.9040 0.000055 0.99983 2.80 105

80 1 0.000544 2 0.9999 0.0108 1.1289 0.000071 0.99998 4.30 106

70 1 0.000544 2 0.9983 0.0062 1.1746 0.000143 0.99984 4.68 105

60 1 0.000544 2 0.9984 0.0054 1.1558 0.000068 0.99997 8.18 106

80 1 0.001250 2 0.9998 0.0100 0.9896 0.000103 0.99994 1.24 105

70 1 0.001250 2 0.9973 0.0107 0.9496 0.000073 0.99989 1.99 105

60 1 0.001250 2 1.0071 0.0094 0.9435 0.000059 0.99987 2.33 105


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for pumpkin,

a 0:966467 0:000184 T 0:007014 V 13k 0:005645 0:000095 T 0:003791 V 14

n 0:572175 0:009074 T 0:064652 V 15

b 0:000050 0:000001 T 0:000024 V 16

These expressions can be used to estimate the mois-

ture ratio of potato, apple and pumpkin slices at any

time during the drying process with a great accuracy.

The consistency of the model and relationship between

the coefficients and drying variables evident with

rpotato 0:9984; v2

potato

2:26 104 and

rapple 0:9976; v2apple 4:03 10

4 and

rpumpkin 0:9955; v2pumpkin 7:76 10

4

5. Conclusion

In order to explain the drying behavior and develop

the mathematical modeling of agricultural products as

potato, apple and pumpkin, 13 models in the literature

were applied. Among these models, in each of three

products, the MidilliKucuk model gave the best results

and showed good agreement with the experimental data

obtained from the experiments including the thin layer

drying process. When the effects of drying air tempera-

ture, velocity and sample area on the constants and

coefficients of the MidilliKucuk model were examined,

the resulting model gave an r of 0.9984 and v2 of

2.26 104 for potato slices, and an r of 0.9976 and v2

of 4.03 104 for apple slices, and an r of 0.9955 and

v2 of 7.76 104 for pumpkin slices. According to re-

sults, it can be said that the MidilliKucuk model ade-

quately described the drying behavior of potato, apple

and pumpkin slices in the drying process at a tempera-

ture range 6080 C and a velocity range 11.5 m/s of

drying air.

Acknowledgement

The author thanks Prof. Ibrahim Dincer from the

University of Ontario Institute of Technology and Dr.

Adnan Midilli from Nigde University, and Firat Univer-

sity Research Foundation (FUNAF) financial support,

under project number 357.

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Table 6

Values of the drying constant and coefficients of the MidilliKucuk model determined through regression method for pumpkin slices at all drying

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